
\section{Performance Evaluation}\label{simulation}
In this section, we first conducted simulations to evaluate the performance of S-KT when estimating the cardinality of remaining key tags and that of missing key tags, respectively. Then, we implement a prototype of S-KT to evaluate its practical deployability.

\subsection{Simulation Settings}
The simulators were implemented via MATLAB on a ThinkPad X230 desktop with an Intel i5 3230M CPU and 8G RAM. In the following, we first conduct a comparison on execution time between S-KT and prior schemes: CATS~\cite{r81}, ITSP~\cite{r82}, ZDE~\cite{r83} and INC~\cite{WeiGong}. Note that, because the identification-based protocols are far from efficiency, we do not compare the proposed S-KT with them. Compared with the delay of wireless data transmission, the time consumed by computing on both the reader side and the tag side is so minor, and thus is neglected. Therefore, we only consider the time consumed by the wireless communications between the reader and the tags. Moreover, the same as the literature \cite{r81} \cite{r82} \cite{r83}~\cite{WeiGong}, we consider an error-free communication channel. Then, we conduct experiments to show that S-KT indeed achieves the required estimation accuracy. Each simulation is independently repeated 1000 times and we report the average~results.


%\begin{figure}
%\subfigure[the second subfigure]{
%\begin{minipage}[b]{0.2\textwidth}
%\includegraphics[width=1\textwidth]{ImpactOfUOnST3S.eps} \\
%\includegraphics[width=1\textwidth]{ImpactOfTOnST3S.eps}
%\end{minipage}
%}
%\end{figure}

%\begin{figure}
%  \subfigure[Small Box with a Long Caption]{
%    \label{fig:mini:subfig:a} %% label for first subfigure
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%      \centering
%      \includegraphics[width=1in]{graphic.eps}
%    \end{minipage}}%
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%    \end{minipage}}
%  \caption{Minipages Inside Subfigures}
%  \label{fig:mini:subfig} %% label for entire figure
%\end{figure}

\subsection{Performance When Estimating $r$}
\subsubsection{Execution time}
In this section, we conduct simulations to evaluate the time-efficiency of the proposed S-KT protocol when estimating the remaining key tag population $r$. Previous work CATS and ITSP need the value of $c$ (i.e., $|S_C|$) to optimize the parameter settings. Then, Zheng \emph{et al.} proposed a light-weight scheme to roughly estimate $c$ thereby providing input for CATS~\cite{r81}. Chen \emph{et al.} directly borrowed the efficient cardinality estimation protocol ART to estimate $c$~\cite{r82}. To their favor, we do not take these time cost into account and configure their parameters directly using the actual $c$. 

\textbf{Investigating the Impact of $u$}. In the simulations corresponding to Fig.~\ref{ImpactOfUOnST3S1}, we aim at investigating the impact of $u$ on the execution time needed by each scheme to estimate the remaining key tag population $r$. Specifically, $u_{max}$ is fixed to $600,000$, which is large enough for common applications. The actual $u$ varies from $100,000$ to $500,000$. The cardinality $k$ of key tags is set to $50,000$. The $d_{max}$ is set to $8$, and the actual $d$ is configured to $1$. We make two main observations from the results shown in Fig.~\ref{ImpactOfUOnST3S1}. First, the performance of CATS, ITSP and the proposed S-KT is not sensitive to $u$, whereas, the execution time of ZDE and INC increases linearly with respect to $u$. And the proposed S-KT is faster than than all prior schemes in all these configurations. For example, as illustrated in Fig.~\ref{ImpactOfUOnST3S1} (b), when $u=500,000$, the execution time of CATS, ITSP, ZDE is 151.1s, 108.7s, 68.8s, respectively. Note that, the execution time of INC exceeds the bounds of the Fig.~\ref{ImpactOfUOnST3S1}~(b) when $u=500,000$. And the execution time of S-KT is just 5.3s, which represents 28.5 times faster than CATS, 20.5 times faster than ITSP, 13 times faster than ZDE. Second, by comparing Fig.~\ref{ImpactOfUOnST3S1}(a) and (b), we observe that the higher the required estimation accuracy is, the longer the execution time is, which also holds on for other schemes.

%\begin{figure*}[!t]
%\centering
%  \subfigure[Estimating $r$: (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$]{\includegraphics[width=0.45\linewidth]{fig/ImpactOfUOnST3S}}
%  \subfigure[Estimating $m$: (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$]{\includegraphics[width=0.47\linewidth]{fig/EstMImpactOfUOnST3S}}
%    \vspace{-10pt}
%  \caption{Time \emph{vs.} $u$: $t=50,000$, $d=1$, $u$ varies from $100,000$ to $500,000$.}
%  \label{ImpactOfUOnST3S}
%\end{figure*}

%
\begin{figure}[!htpb]
\centerline{\includegraphics[scale=0.55]{fig/ImpactOfUOnST3S}}
\vspace{-0.1in}
\caption{Estimation of $r$. Time \emph{vs.} $u$: $k=50,000$, $d_{max}=8$, $d=1$, $u_{max}=600,000$, $u$ varies from $100,000$ to $500,000$. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
\label{ImpactOfUOnST3S1}
\end{figure}


\textbf{Investigating the Impact of $k$}. In the simulations corresponding to Fig.~\ref{ImpactOfTOnST3S}(i), we aim at investigating the impact of $k$ on the execution time needed by each scheme to estimate the remaining key tag population $r$. Specifically, $u_{max}$ is still fixed to $600,000$, and the actual $u$ is set to $300,000$. The $d_{max}$ is fixed to $8$, and the actual $d$ is set to $1$. The cardinality $k$ of the key tags varies from $30,000$ to $70,000$. We make two main observations from the results shown in Fig.~\ref{ImpactOfTOnST3S}(i)(a) and (i)(b). First, the execution time of CATS and ITSP increases linearly with respect to $k$. In contrary, the execution time of ZDE, INC and our S-KT decreases with respect to $k$. The underlying reason is that a larger $k$ increases the ratio of $\frac{r}{u}$, which facilitates the estimation of $r$. Second, the proposed S-KT persistently outperforms the prior schemes with different $k$, which reveals its good scalability. As illustrated in Fig.~\ref{ImpactOfTOnST3S}~(b), when $t=70,000$, the execution time of CATS, ITSP, ZDE is 206.4s, 143.9s, and 35.1s, respectively. Note that, because the execution time of INC \emph{exceeds} the bounds of the Fig.~\ref{ImpactOfTOnST3S}(i)(b), the corresponding line does not appear. The execution time of S-KT is just 3.6s, which represents 57.3 times faster than CATS, 40 times faster than ITSP, 9.8 times faster than ZDE. Fig.~\ref{ImpactOfTOnST3S}(ii) show the performance of each scheme when estimating the missing key tag population $m$ with different $k$.
\begin{figure}[!htpb]
\centerline{\includegraphics[scale=0.55]{fig/ImpactOfTOnST3S}}
\vspace{-0.1in}
\caption{Estimation of $r$. Time \emph{vs.} $k$: $d_{max}=8$, $d=1$, $u_{max}=600,000$, $u=300,000$, $k$ varies from $30,000$ to $70,000$. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
\label{ImpactOfTOnST3S}
\end{figure}




%\begin{figure*}[!t]
%\centering
%  \subfigure[Estimating $r$: (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$]{\includegraphics[width=0.45\linewidth]{fig/ImpactOfTOnST3S}}
%  \subfigure[Estimating $m$: (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$]{\includegraphics[width=0.47\linewidth]{fig/EstMImpactOfTOnST3S}}
%    \vspace{-10pt}
%  \caption{Time \emph{vs.} $k$: $d_{max}=8$, $d=1$, $u_{max}=600,000$, $u=300,000$, $k$ varies from $30,000$ to $70,000$.}
%  \label{ImpactOfTOnST3S}
%\end{figure*}


\textbf{Investigating the Impact of $d$}. In the simulations corresponding to Fig.~\ref{ImpactOfDOnST3S}(i), we aim at investigating the impact of $d$ on the execution time needed by each scheme to estimate the remaining key tag population $r$. Specifically, $u_{max}$ is still fixed to $600,000$, and the actual $u$ is set to $300,000$. The cardinality $k$ of key tags is set to $50,000$. The upper bound $d_{max}$ of $d$ is configured to $8$, and the actual $d$ varies from $\frac{1}{4}$ to $4$ in log-scale. According to Fig.~\ref{ImpactOfDOnST3S} (a) and (b), we observe that the proposed S-KT is significantly faster than all prior schemes. As illustrated in Fig.~\ref{ImpactOfDOnST3S} (b), when $d=4$, the execution time of CATS, ITSP, ZDE is 207.9s, 72.7s, 109.9s, respectively. Again, the line corresponding to INC does not appear in Fig.~\ref{ImpactOfDOnST3S} (b) because it exceeds the bounds of figure. And the execution time of S-KT is just 14.5s, which represents 13.3 times faster than CATS, 5 times faster than ITSP, and 7.6 times faster than ZDE. Fig.~\ref{ImpactOfDOnST3S}(ii) show the performance of each scheme when estimating the missing key tag population $m$ with different $d$.
\begin{figure}[!htpb]
\centerline{\includegraphics[scale=0.55]{fig/ImpactOfDOnST3S}}
\vspace{-0.1in}
\caption{Estimation of $r$. Time vs. $d$: $k=50,000$, $u_{max}=600,000$, $u=300,000$, $d_{max}=8$, $d$ varies from $\frac{1}{4}$ to $4$ in logscale. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
\label{ImpactOfDOnST3S}
\end{figure}

%
%
%
%\begin{figure*}[!t]
%\centering
%  \subfigure[Estimating $r$: (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$]{\includegraphics[width=0.45\linewidth]{fig/ImpactOfDOnST3S}}
%  \subfigure[Estimating $m$: (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$]{\includegraphics[width=0.47\linewidth]{fig/EstMImpactOfDOnST3S}}
%    \vspace{-10pt}
%  \caption{Time \emph{vs.} $d$: $k=50,000$, $u_{max}=600,000$, $u=300,000$, $d_{max}=8$, $d$ varies from $\frac{1}{4}$ to $4$ in logscale.}
%  \label{ImpactOfDOnST3S}
%\end{figure*}
%%
%\begin{figure}[t]
%\centerline{\includegraphics[scale=0.55]{PerformanceOfST3S1.eps}}
%\caption{Time vs. $u$: $t=50,000$, $d=1$, $u$ varies from $100,000$ to $500,000$. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
%\label{time1}
%\end{figure}
%
%\begin{figure}[t]
%\centerline{\includegraphics[scale=0.55]{PerformanceOfST3S2.eps}}
%\caption{Time vs. $t$: $d=1$, $u=300,000$, $t$ varies from $30,000$ to $70,000$. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
%\label{time2}
%\end{figure}
%
%\begin{figure}[t]
%\centerline{\includegraphics[scale=0.55]{PerformanceOfST3S3.eps}}
%\caption{Time vs. $d$: $t=50,000$, $u=300,000$, $d$ varies from $\frac{1}{4}$ to $4$. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
%\label{time3}
%\end{figure}

\subsubsection{Actual Reliability}
The parameters $(\alpha,\beta)$ given as input of S-KT indicate the \emph{required accuracy}. The estimation accuracy that an estimation scheme achieves is referred to as its \emph{actual reliability}. This section conducts simulations to evaluate the actual reliability of the proposed S-KT. Specifically, for each parameter setting, we conducted 1000 independent simulations. In an arbitrary simulation, if the estimation result $\hat{r}$ (or $\hat{m}$) satisfies $(\alpha,\beta)$ accuracy, we refer to it as a \emph{success estimation}. We record the \emph{success times} among 1000 times. We use the ratio of $\frac{success~times}{1000}$ to measure the \emph{actual reliability}. The simulation results shown in Figs. \ref{ImpactOfUOnReliability}, \ref{ImpactOfTOnReliability} and \ref{ImpactOfDOnReliability} demonstrate that the proposed S-KT still persistently meets the required accuracy.

%\begin{figure*}[!t]
%\centering
%  \subfigure[Estimating $r$: (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$]{\includegraphics[width=0.45\linewidth]{fig/ImpactOfUOnReliability}}
%  \subfigure[Estimating $m$: (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$]{\includegraphics[width=0.47\linewidth]{fig/ImpactOfUOnReliability(2)}}
%    \vspace{-10pt}
%  \caption{Actual accuracy \emph{vs.} $u$: $k=50,000$, $d_{max}=8$, $d=1$, $u_{max}=600,000$, $u$ varies from $100,000$ to $500,000$.}
%  \label{ImpactOfUOnReliability}
%\end{figure*}

\begin{figure}[!htpb]
\centerline{\includegraphics[scale=0.55]{fig/ImpactOfUOnReliability}}
\vspace{-0.1in}
\caption{Estimation of $r$. Actual reliability \emph{vs.} $u$: $k=50,000$, $d_{max}=8$, $d=1$, $u_{max}=600,000$, $u$ varies from $100,000$ to $500,000$. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
\label{ImpactOfUOnReliability}
\end{figure}


%
%\begin{figure*}[!t]
%\centering
%  \subfigure[Estimating $r$: (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$]{\includegraphics[width=0.45\linewidth]{fig/ImpactOfTOnReliability}}
%  \subfigure[Estimating $m$: (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$]{\includegraphics[width=0.47\linewidth]{fig/ImpactOfTOnReliability(2)}}
%    \vspace{-10pt}
%  \caption{Actual accuracy vs. $k$: $d_{max}=8$, $d=1$, $u_{max}=600,000$, $u=300,000$, $k$ varies from $30,000$ to $70,000$.}
%  \label{ImpactOfTOnReliability}
%\end{figure*}


\begin{figure}[!htpb]
\centerline{\includegraphics[scale=0.55]{fig/ImpactOfTOnReliability}}
\vspace{-0.1in}
\caption{Estimation of $r$. Actual reliability \emph{vs.} $k$: $d_{max}=8$, $d=1$, $u_{max}=600,000$, $u=300,000$, $k$ varies from $30,000$ to $70,000$. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
\label{ImpactOfTOnReliability}
\end{figure}


%
%\begin{figure*}[!t]
%\centering
%  \subfigure[Estimating $r$: (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$]{\includegraphics[width=0.45\linewidth]{fig/ImpactOfDOnReliability}}
%  \subfigure[Estimating $m$: (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$]{\includegraphics[width=0.47\linewidth]{fig/ImpactOfDOnReliability(2)}}
%  \vspace{-10pt}
%  \caption{Actual accuracy vs. $d$: $k=50,000$, $u_{max}=600,000$, $u=300,000$, $d_{max}=8$, $d$ varies from $\frac{1}{4}$ to $4$ in logscale.}
%  \label{ImpactOfDOnReliability}
%\end{figure*}

\begin{figure}[!htpb]
\centerline{\includegraphics[scale=0.55]{fig/ImpactOfDOnReliability}}
\vspace{-0.1in}
\caption{Estimation of $r$. Actual reliability \emph{vs.} $d$: $k=50,000$, $u_{max}=600,000$, $u=300,000$, $d_{max}=8$, $d$ varies from $\frac{1}{4}$ to $4$ in logscale. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
\label{ImpactOfDOnReliability}
\end{figure}



\subsection{Performance When Estimating $m$}
In this section, we conduct simulations to evaluate the performance of our S-KT when estimating the missing key tag population $m$.

\subsubsection{Execution time}
Since INC \cite{WeiGong} cannot estimate the missing key tag population with guaranteed $(\alpha,\beta)$ accuracy, we do not compare our S-KT protocol with it in this set of simulations. Here, we use CATS, ITSP, ZDE as the benchmark protocols. Again, we conduct the simulations under different parameters $u$, $k$ and $d$.

\textbf{Investigating the Impact of $u$}
In the simulations corresponding to Fig.~\ref{ImpactOfUWhenEstM}, our objective is to study the impact of $u$ on the performance of S-KT when estimating $m$. $u_{max}$ is set to 600,000. The actual $u$ varies from 100,000 to 500,000. The concerned key tag number $k$ is 50,000. $d_{min}$ is set to $\frac{1}{8}$. We have two main observations from the simulation results. First, our S-KT is still of great scalability when estimating the missing key tag population. In contrary, the execution time of ZDE increases sharply with the increase of $u$. Hence, our S-KT protocol is more suitable for large-scale RFID systems. Second, our S-KT protocol consistently runs faster than all the other protocols.
\begin{figure}[h]
\centerline{\includegraphics[scale=0.55]{fig/EstMImpactOfUOnST3S}}
\vspace{-0.1in}
\caption{Estimation of $m$. Time \emph{vs.} $u$: $k=50,000$, $d_{min}=\frac{1}{8}$, $d=1$, $u_{max}=600,000$, $u$ varies from $100,000$ to $500,000$. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
\label{ImpactOfUWhenEstM}
\end{figure}

\textbf{Investigating the Impact of $k$}
In this set of simulations, we investigate the impact of key tag number $k$ on the protocol performance. $u_{max}$ is still set to 600,000. The actual $u$ is 300,000. $d_{min}$ is $\frac{1}{8}$. The actual $d$ is 1. The key tag number $k$ varies from 30,000 to 70,000. We observe that the execution time of CATS and ITSP increases sharply with respect to the key tag number. The underlying reason is that the filter length should be proportional to the increasing key tag number in order to guarantee the filtering accuracy. In contrary, the time cost of ZDE and our S-KT decreases against the number of key tags. Our S-KT protocol still runs several times faster than all the other protocols.
\begin{figure}[h]
\centerline{\includegraphics[scale=0.55]{fig/EstMImpactOfTOnST3S}}
\vspace{-0.1in}
\caption{Estimation of $m$. Time \emph{vs.} $k$: $d_{min}=\frac{1}{8}$, $d=1$, $u_{max}=600,000$, $u=300,000$, $k$ varies from $30,000$ to $70,000$. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
\label{ImpactOfTWhenEstM}
\end{figure}

\textbf{Investigating the Impact of $d$}
In this set of simulations, we investigate the impact of key tag number $d$ on the protocol performance. $u_{max}$ is still set to 600,000. The actual $u$ is 300,000. The key tag number $k$ is 50,000. $d_{min}$ is $\frac{1}{8}$. The actual $d$ varies from $\frac{1}{4}$ to 4. The simulation results shown in Fig.~\ref{EstMImpactOfDOnST3S} reveal that a larger $d$ (i.e., $\frac{m}{r}$) will decrease the time cost when estimating the missing key tag population. Our S-KT protocol still runs several times faster than the other protocols.
\begin{figure}[!htpb]
\centerline{\includegraphics[scale=0.55]{fig/EstMImpactOfDOnST3S}}
\vspace{-0.1in}
\caption{Estimation of $m$. Time \emph{vs.} $d$: $k=50,000$, $u_{max}=600,000$, $u=300,000$, $d_{min}=\frac{1}{8}$, $d$ varies from $\frac{1}{4}$ to $4$ in logscale. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
\label{EstMImpactOfDOnST3S}
\end{figure}

\subsubsection{Actual reliability}
In this set of simulations, we aim at evaluating the actual reliability of our estimator $\hat{m}$ under different parameter settings. The simulation results shown in Figures \ref{ImpactOfUOnReliabilityEstM}, \ref{ImpactOfTOnReliabilityEstM} and \ref{ImpactOfDOnReliabilityEstM} demonstrate that the proposed S-KT always meets the required accuracy when estimating the missing key tag population $m$.

\begin{figure}[h]
\centerline{\includegraphics[scale=0.55]{fig/ImpactOfUOnReliability(2)}}
\vspace{-0.1in}
\caption{Estimation of $m$. Actual reliability \emph{vs.} $u$: $k=50,000$, $d_{max}=8$, $d=1$, $u_{max}=600,000$, $u$ varies from $100,000$ to $500,000$. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
\label{ImpactOfUOnReliabilityEstM}
\end{figure}

\begin{figure}[h]
\centerline{\includegraphics[scale=0.55]{fig/ImpactOfTOnReliability(2)}}
\vspace{-0.1in}
\caption{Estimation of $m$. Actual reliability \emph{vs.} $k$: $d_{max}=8$, $d=1$, $u_{max}=600,000$, $u=300,000$, $k$ varies from $30,000$ to $70,000$. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
\label{ImpactOfTOnReliabilityEstM}
\end{figure}

\begin{figure}[h]
\centerline{\includegraphics[scale=0.55]{fig/ImpactOfDOnReliability(2)}}
\vspace{-0.1in}
\caption{Estimation of $m$. Actual reliability \emph{vs.} $d$: $k=50,000$, $u_{max}=600,000$, $u=300,000$, $d_{max}=8$, $d$ varies from $\frac{1}{4}$ to $4$ in logscale. (a) $\alpha=10\%$, $\beta=90\%$; (b) $\alpha=5\%$, $\beta=95\%$.}
\label{ImpactOfDOnReliabilityEstM}
\end{figure}

\subsection{Prototype Implementation}
We use the highly integrated ultra low power 2.4GHz RF System-on-Chip (SoC) nRF24LE1 \cite{nRF24LE1} to implement a prototype of our S-KT, which is shown in Fig.~\ref{prototype}. nRF24LE1 includes a 2.4GHz RF transceiver core, an 8-bit CPU, and embedded Flash memory. The computer and the reader communicate via RS232 serial port. The tags are active and powered by button cells. The prototype also includes a simple user interface on the computer side, by which the end users can configure the required estimation accuracy and get the estimation result. The implemented RFID system includes one RFID reader and 20 RFID tags. The specified key tag list contains 20 potential IDs. The number of remaining key tags are fixed to 12, and thus the number of missing key tags is 8. We conduct two set of experiments to evaluate the practical performance of our S-KT protocol when estimating $r$ and $m$, respectively. As shown in Fig.~\ref{PerformanceOfPrototype}(i)(a), 95 results among 100 simulations meet the predefined estimation accuracy ($\alpha=0.1$). And in Fig.~\ref{PerformanceOfPrototype}(ii)(a), 92 results among 100 simulations meet the predefined estimation accuracy ($\alpha=0.1$). The ratio of success time to 100 is higher than the required reliability ($\beta=90\%$) when estimating either $r$ or $m$.

\begin{figure}[h]
\centerline{\includegraphics[scale=0.14]{fig/prototype1.eps}}
\caption{The implemented prototype of our S-KT.}
\label{prototype}
\end{figure}

\renewcommand{\thesubfigure}{\roman{subfigure}} \makeatletter
\renewcommand{\@thesubfigure}{(\thesubfigure)\space}
\renewcommand{\p@subfigure}{\thefigure} \makeatother
\begin{figure*}[!thb]
\centering
  \subfigure[Estimation of $r$: (a) Estimation accuracy; (b) Execution time]{\includegraphics[width=0.45\linewidth]{fig/EstimateR}}
  \subfigure[Estimation of $m$: (a) Estimation accuracy; (b) Execution time]{\includegraphics[width=0.45\linewidth]{fig/EstimateM}}
  \vspace{-0.1in}
  \caption{{Evaluating the performance of our prototype. $u_{max}$=50; $d_{max}$=4; $d_{min}$=1/4; $\alpha$=10\%; $\beta$=90\%; $r$=8; $m$=12; $o$=8.}}
  \label{PerformanceOfPrototype}
  \vspace{-10pt}
\end{figure*}
